Smith went 21-of-34 through the air for 173 yards and Jamaal Charles ran for 77 yards on 16 carries as Kansas City (1-0) corralled a win in a game that also featured the first appearance for new Chiefs head Coach Andy Reid.
Reid replaced Romeo Crennel, who was fired after Kansas City went 2-14 last season -- tied with the Jaguars for worst in the NFL.
Jacksonville's Blaine Gabbert managed to complete just 16-of-35 passes for 121 yards with a pair of interceptions before leaving the game in the fourth quarter with an apparent arm injury.
Maurice Jones-Drew picked up 45 yards on 15 carries for the Jaguars (0-1), who fell in the debut of their new head coach, Gus Bradley, who replaced the fired Mike Mularkey.
Swim Week Miami Beach 2014 [PHOTOS]